Grey-Box Bayesian Optimization Improves Efficiency with Separability

This paper presents a novel approach to grey-box optimization problems, where decision variables can be naturally divided into two categories: black-box variables that feed into an expensive, opaque function, and white-box variables governed by explicit, closed-form equations. The core idea is a bilevel optimization strategy. An outer Bayesian optimization process handles the black-box variables, aiming to optimize the overall objective. Concurrently, an inner global optimization problem addresses the white-box variables, ensuring their constraints are precisely met. This method avoids common pitfalls like penalty functions or approximations. The proposed bilevel Bayesian optimization framework demonstrates superior performance across a suite of 13 benchmark problems. It consistently achieves lower regret, requires fewer iterations, and reduces overall wall-clock time compared to existing methods. The advantages hold true regardless of the initial dataset size, exploration parameters, or the specific inner-solver chosen, highlighting its robustness and efficiency in complex optimization scenarios.